A354559 The number of terms of A354558 that are <= 10^n.

1, 2, 5, 13, 28, 79, 204, 549, 1509, 4231, 12072, 36426, 112589

Offset

1,2

Comments

The data is from De Koninck et al. (2013).

Links

Table of n, a(n) for n=1..13.

Jean-Marie De Koninck, Nicolas Doyon, and Florian Luca, Consecutive integers divisible by the square of their largest prime factors, Journal of Combinatorics and Number Theory, Vol. 5, No. 2 (2013), pp. 81-93; Researchgate link.

Jean-Marie De Koninck and Matthieu Moineau, Consecutive Integers Divisible by a Power of their Largest Prime Factor, J. Integer Seq., Vol. 21 (2018), Article 18.9.3.

Régis de la Bretèche and Sary Drappeau, Niveau de répartition des polynômes quadratiques et crible majorant pour les entiers friables, Journal of the European Mathematical Society, Vol. 22, No. 5 (2020), pp. 1577-1624; arXiv preprint, arXiv:1703.03197 [math.NT], 2017-2019.

Example

There is one term <= 10 in A354558, 8, therefore a(1) = 1.
There are 2 terms <= 10^2 in A354558, 8 and 49, therefore a(2) = 2.

Mathematica

q[n_] := FactorInteger[n][[-1, 2]] > 1; c[s_, n_] := Count[s, _?(# <= n &)]; m = 6; c[Select[Range[10^m], q[#] && q[# + 1] &], #] & /@ (10^Range[m])

Crossrefs

Cf. A354558.

Sequence in context: A290194 A241392 A319778 * A002559 A049097 A045366

Adjacent sequences: A354556 A354557 A354558 * A354560 A354561 A354562

Keyword

nonn,more

Author

Amiram Eldar, May 30 2022

Extensions

a(12) from Daniel Suteu, Jun 03 2022

a(13) from Daniel Suteu, Jun 05 2022

Status

approved